Put picture from imported pic as vertex paint and engrave / extrude the shape from other object
Usually this is how I do it....

Convert the Jpg or Png into SVG format. You can find a
free online converter on google search. Keyword to search
is "Converter Jpeg to SVG" or "Converter Png to SVG".

You can then import the SVG format as a spline. With the
spline, you could then convert it to mesh. Fill those faces
and extrude those faces.

To cut the words into a cube, you would use the boolean or
booltool ( An easier and a better way to work) in Blender
to accomplish the task.

NOTE:

You may have to watch a few topics on youtube on the subject
I have pointed you to. Else there will be too much instruction
to write up.